Mathematics,manifest: a review of Mathematics: the Winton Gallery at the Science Museum

Mathematics: the Winton Gallery strives, like any exhibition concerning mathematics, to make meaningful contact between the abstruse realms of mathematics and the viewing audience. Unlike many other exhibitions, this is here accomplished by displaying a rich range of objects that demonstrate the essential role of mathematics in the world by emphasizing connections to the viewers’ existing cognitive environments. Through a focus on the ways that mathematical work affects and informs our human world, the exhibition succeeds in connecting a mathematical way of thinking with the lives of the viewing public in a complex and profound way, in exchange for their efforts and attention. While an approach which places the interweave of life and mathematics at its centre may invite worries about the representation of pure mathematics or whether such a strategy insulates the viewer from an understanding of ‘real’ mathematics, what this exhibition does is to offer a sense of the mind-set that underscores mathematical work. By revealing the implications of this mode of thought, the exhibition encourages the audience to understand their own lives and world in a more mathematically-oriented way, while also encouraging them to understand mathematics in terms of the ways their human world is already formed.     

Mathematics education: Procedures, rituals and man's search for meaning

An attempt is made to analyze mathematical behavior from more general psychological perspectives. The mathematical language is a special case of the human language, which is a form of expression. Many people use common language in a meaningless way. The same is true about the mathematical language. Rituals are other forms of expression. Many people identify rituals in many mathematical contexts (procedures, argumentation). Thus, quite often, they behave in a meaningless way as required by many rituals. On the other hand, the community of mathematics education struggles for meaningful learning. This can be regarded as a special case of man's search for meaning. The general claims will be illustrated by some examples from various mathematical contexts.     

Ranking countries according to economic,social and political indicators

Despite its inadequacies, the GNP is still the best known and most widely used economic indicator to measure development. A number of authors have considered otherrelevant indicators, such as life expectancy, infant mortality, literacy and so on, as measures of development. In this paper we offer a composite index that touches more on the quality of life to measure the degree of development of the nations of the world. The criteria used here are: GNP per capita, physical quality of life, percentage of national income received by the poorest 40%, population density in agricultural areas, political rights and civil liberties, No. of telephones per capita and No. of drug-related offenses. We then used absolute measurement to obtain a composite index for each of nearly two dozen nations. The U.S.A. ranked second to Australia.     

Socio-economic and cultural mediators of mathematics achievement and between-school equity in mathematics education at the global level

This paper aims at identifying and understanding how and to what extent socioeconomic and cultural factors mediate mathematics achievement and between-school equity in mathematics education among countries. First, under the assumption that equity and quality of education are independent constructs, the construct of equity-in-quality in mathematics education is developed. Second, the 18 countries that were identified in the previous work of the author Jurdak in (Toward equity in quality in mathematics education. Springer, New York, 2009) as being diverse in mathematics education will serve as study cases to illustrate, compare, and contrast the mediatory role of socio-economic and cultural factors in mathematics achievement and between-school equity in mathematics education. The results show that the differences in mathematics achievement and between-school equity in mathematics education at the country level are associated with, and can be accounted for in some cases, by socioeconomic and cultural factors.     

Mathematics education research, its nature, and its purpose: A discussion of Lester's paper

This commentary discusses the framework for mathematics education researchers outlined in Lester's (2005) paper. The author reacts to (a) Lester's concern about the current political forces in the U.S. to define scientific research in education rigidly, and offers a possible reason—apart from political ideology—for the emergence of hese forces; (b) recapitulates lester's outline and model for theory-based research in mathematics education, and intereprets Lester's paper as a call to the MER community to respond to the current political forces that (inappropriately) shape our field and (c) addresses the role of mathematical context in MER, a topic absent from the paper's narrative.     

Mathematics teacher education advanced methods: an example in dynamic geometry

We present a research work about an innovative national teacher training program in France: the Pairform@nce program, designed to sustain ICT integration. We study here training for secondary school teachers, whose objective is to foster the development of an inquiry-based approach in the teaching of mathematics, using investigative potentialities of dynamic geometry environments. We adopt the theoretical background of the documentational approach to didactics. We focus on the interactions between teachers and resources: teachers’ professional knowledge influences these interactions, which at the same time yield knowledge evolutions, a twofold process that we conceptualise as a documentational genesis. We followed in particular the work of a team of trainees; drawing on the data collected, we analyse their professional development, related with the training. We observe intertwined evolutions and stabilities, consistent with ongoing geneses.     

A brief history of mathematics education in Turkey: K-12 mathematics curricula

In this study, we survey the history of mathematics education in Turkey starting with its historical roots in the foundation of the republic. The changes in mathematics education in Turkey over the last century are investigated through an analysis of changes in curricular documents for K-12 schools. We consider the factors and reasons affecting curriculum developments, changes in philosophy and structure in terms of standards, objective and instructions. This article utilizes archival research techniques by examining original sources and illustrates the nature of the changes benefiting from a historical perspective. As a result of such analysis of the aforesaid sources, we have seen that the main reasons for changing mathematics curricula are: to build up a modern civilization in Turkey; the reports of John Dewey and the recommendations of Kate Wofford, William C. Varaceus and Watson Dickerman; the desire to become a member of the European Union; international factors and political situations.     

An analysis of history of mathematics research literature in Turkey: the mathematics education perspective1

Research in history of mathematics gained momentum in the past two decades in Turkey. The present paper aims to describe the patterns in the history of mathematics research in Turkey and to analyse the research in Turkey using a mathematics education framework. The qualitative paradigm and a case study design are used in the study. The obtained data were analysed by using the document analysis technique with the help of a content analysis. The study group which is comprised of twenty-two postgraduate theses at master's or doctoral level were purposefully selected from the higher education council postgraduate theses database. Findings indicate a dearth of research in the area and that most of the theses are done in the area of mathematics education. Moreover, the focus, in general, was on attitudinal variables, and cognitive aspects seemed to be ignored.     

Commentary to Lesh and Sriraman: Mathematics education as a design science

In this commentary, the author discusses the strengths and weaknesses to Lesh & Sriraman's (2005) ambitious proposal of re-conceptualizing the field of mathematics education research as that of a design science.     

Exploration of technologies, emerging from African cultural practices, in mathematics (teacher) education

The study at teacher education institutions in Africa of mathematical ideas, from African history and cultures, may broaden the horizon of (future) mathematics teachers and increase their socio-cultural self-confidence and awareness. Exploring educationally mathematical ideas embedded in, and derived from, technologies of various African cultural practices may contribute to bridge the gap between ‘home’ and ‘school’ culture. Examples of the study and exploration of these technologies and cultural practices will be presented. The examples come from cultural practices as varied as story telling, basket making, salt production, and mat, trap and hat weaving.     

Mathematics of currency and exchange: arithmetic at the end of the thirteenth century

In western Europe, a sophisticated banking system for the purposes of international trade had evolved by the end of the thirteenth century. It was based upon the ‘bill of exchange’, which enabled an exporter of goods to receive payment in his own currency, by means of a balancing payment made in the currency of the importer. This paper discusses the arithmetical tools that were available for use in accounting for transactions made in different currencies. It is argued that algorithmic methods based on the Hindu-Arabic numerals were used at the higher levels of banking, in order to prepare tables of foreign exchange such as those collected by the Florentine banker, Francesco Pegolotti. On the other hand, the clerks who were responsible for routine book-keeping would have used a simple abacus and counters, and recorded their transactions in Roman numerals. The paper is based on a talk given to the BSHM at Gresham College on 25 April 2008.     

Teacher-student interaction: A game theoretic extension of the economic theory of education

This paper employs the ‘economic theory of education’ to consider the joint interactive choices of student and teacher. Game theoretic analysis is applied extending the work begun by Correa (1974). It is shown that the relative degree of substitutability in the utility and achievement functions determines whether a student responds positively or negatively to the teacher's greater effort or harder grading. Conditions for the existence and stability of a non-cooperative equilibrium are investigated. Due to the public good nature of student achievement, the non-cooperative equilibrium will result in insufficient academic effort being allocated to academic achievement for Pareto optimality; and therefore, there is a need for binding cooperative agreements.     

Using E-Exercise Bases in Mathematics: Case Studies at University

E-Exercise Bases (EEB) are now used in the teaching of mathematics, especially at university. We discuss here the consequences of their use on the students’ activity during computer lab sessions. Results stem from observations of several teaching designs organised in different French universities with three e-exercise bases. The analysis focuses on new tasks and on specific solving strategies, which appear using these resources. Moreover, specific didactic contract clauses are studied.